硬币系列,放一些做过的
【2019城市数学奥林匹克】There are 100 visually identical coins of three types: golden, silver and copper. There is at least one coin of each type. Each golden coin weighs 3 grams, each silver coins weighs 2 grams and each copper coin weighs 1 gram. How to find the type of each coin performing no more than 101 measurements on a balance scale with no weights.
有100枚外观完全相同的硬币,分为金银铜三种类型,每种类型至少一枚,每枚金币重3克,每枚银币重2克,每枚铜币重1克。现有一个无砝码的天平,允许称重不超过101次,如何分辨出每一枚硬币的材质?
【2019全俄】We are given n coins of different weights and n balances,n>2. On each turn one can choose one balance, put one coin on the right pan and one on the left pan, and then delete these coins out of the balance. It's known that one balance is wrong (but it's not known ehich exactly), and it shows an arbitrary result on every turn. What is the smallest number of turns required to find the heaviest coin?
有n各不同重量的硬币和n个天平, 这里n>2。每轮你可以把两个硬币放上一个天平来比较他们的重量,之后把硬币放回去。已知有一个天平坏了(但不知道是哪一个,这个天平每次给出随机结果)求最少的可确保找出最重的硬币的称重次数。
【2019城市数学奥林匹克】There are 100 visually identical coins of three types: golden, silver and copper. There is at least one coin of each type. Each golden coin weighs 3 grams, each silver coins weighs 2 grams and each copper coin weighs 1 gram. How to find the type of each coin performing no more than 101 measurements on a balance scale with no weights.
有100枚外观完全相同的硬币,分为金银铜三种类型,每种类型至少一枚,每枚金币重3克,每枚银币重2克,每枚铜币重1克。现有一个无砝码的天平,允许称重不超过101次,如何分辨出每一枚硬币的材质?
【2019全俄】We are given n coins of different weights and n balances,n>2. On each turn one can choose one balance, put one coin on the right pan and one on the left pan, and then delete these coins out of the balance. It's known that one balance is wrong (but it's not known ehich exactly), and it shows an arbitrary result on every turn. What is the smallest number of turns required to find the heaviest coin?
有n各不同重量的硬币和n个天平, 这里n>2。每轮你可以把两个硬币放上一个天平来比较他们的重量,之后把硬币放回去。已知有一个天平坏了(但不知道是哪一个,这个天平每次给出随机结果)求最少的可确保找出最重的硬币的称重次数。